A half-hour documentary on a Ugandan rebel leader that has been watched by tens of millions online has been broadcast in full on Australian television.

The film's subject is Joseph Kony, leader of Ugandan rebel group the Lord's Resistance Army (LRA). It was posted online by the US-based group Invisible Children, which aimed to use the power of social media to make him "famous" and, by doing so, raise his profile enough so world powers such as the United States were motivated to intervene and help capture him.

In Australia Kony 2012 quickly moved from social media to mainstream TV with an hour-long special on the national television network, Ten, on Thursday evening. The commercial network broadcast the half-hour film uninterrupted, saying it had responded to tweets and the "Kony-fication of our Facebook page".

Kony stands accused of appalling crimes, including the kidnap, torture and rape of children. The LRA began its campaign of terror in northern Uganda more than 20 years ago, originally in what it called a fight for a biblical state and the rights of the Acholi people. Since then Kony has been indicted for crimes against humanity at the international criminal court.

The film's narrator is Invisible Children's Jason Russell. He visited Uganda nearly 10 years ago and met a boy who feared for his life because of Kony. Russell promised the boy he would help stop the LRA and Kony 2012 is part of that campaign.

Russell says Kony is the "most wanted man in the world according to the international criminal court", and his documentary aims to put the name into every household's conversation.

Through lobbying cultural and political leaders in the United States, Invisible Children wants to pressure the White House to continue its assistance to the Ugandan army in capturing Kony. Last year the US sent 100 military advisers to Uganda.

"If the government doesn't know people care, they will not keep them there," Russell says in the film. "They will only know if Kony's name is everywhere."

The film has been criticised in some quarters as promoting neo-colonialism by trying to get outside powers, primarily the US, to intervene to capture Kony. Others have said Kony is no longer believed to be operating in Uganda and, by some accounts, has not been for six years and his LRA is down to just a few hundred men.